Recursive Least-Squares Estimation for the Joint Input-State Estimation of Linear Discrete Time Systems with Unknown Input

This paper presents a recursive least-squares approach to estimate simultaneously the state and the unknown input of linear time varying discrete time systems with unknown input. The method is based on the assumption that no prior knowledge about the dynamical evolution of the input is available. The joint input and state estimation are obtained by recursive least-squares formulation by applying the inversion lemmas. The proposed filter is equivalent to recursive three step filter. To illustrate the performance of the proposed filter an example is given

Modeling of permanent magnet linear generator and state estimation based on sliding mode observer: A wave energy system application

summary:This paper synopsis a new solution for Permanent Magnets Linear Generator (PMLG) state estimation subject to bounded uncertainty. Therefore, a PMLG modeling method is presented based on an equivalent circuit, wherein a mathematical model of the generator adapted to wave energy conversion is established. Then, using the Linear Matrix Inequality (LMI) optimization and a Lyapunov function, this system's Sliding Mode Observer (SMO) design method is developed. Consequently, the proposed observer can give a robust state estimation. At last, numerical examples with and without uncertainty are included to exemplify the effectiveness and applicability of the suggested approaches

Robust Filtering for State and Fault Estimation of Linear Stochastic Systems with Unknown Disturbance

This paper presents a new robust filter structure to solve the simultaneous state and fault estimation problem of linear stochastic discrete-time systems with unknown disturbance. The method is based on the assumption that the fault and the unknown disturbance affect both the system state and the output, and no prior knowledge about their dynamical evolution is available. By making use of an optimal three-stage Kalman filtering method, an augmented fault and unknown disturbance models, an augmented robust three-stage Kalman filter (ARThSKF) is developed. The unbiasedness conditions and minimum-variance property of the proposed filter are provided. An illustrative example is given to apply this filter and to compare it with the existing literature results

Simultaneous Robust Fault and State Estimation for Linear Discrete-Time Uncertain Systems

We consider the problem of robust simultaneous fault and state estimation for linear uncertain discrete-time systems with unknown faults which affect both the state and the observation matrices. Using transformation of the original system, a new robust proportional integral filter (RPIF) having an error variance with an optimized guaranteed upper bound for any allowed uncertainty is proposed to improve robust estimation of unknown time-varying faults and to improve robustness against uncertainties. In this study, the minimization problem of the upper bound of the estimation error variance is formulated as a convex optimization problem subject to linear matrix inequalities (LMI) for all admissible uncertainties. The proportional and the integral gains are optimally chosen by solving the convex optimization problem. Simulation results are given in order to illustrate the performance of the proposed filter, in particular to solve the problem of joint fault and state estimation

Robust parameter estimation with noisy data Robust parameter estimation with noisy data

Abstract. For process control improvement, coherency of information supplied by instrument lines and sensors must first be ensured; because of the presence of random and possibly gross errors, the model equations of the process are not generally satisfied. Moreover, the parameters of the considered model are not always exactly known. The problem of how to reconcile the measurements so that they satisfy the model constraints is considered in this article. The simultaneous presence of measurement errors in process input and output measurements coupled with the model parameter uncertainty poses serious problem in the rectification of data. In that paper, the problem is solved using a special filter to estimate both the parameters, the input and the output of a process represented by an autoregressive model

A NOVEL FUZZY C–REGRESSION MODEL ALGORITHM USING A NEW ERROR MEASURE AND PARTICLE SWARM OPTIMIZATION

This paper presents a new algorithm for fuzzy c-regression model clustering. The proposed methodology is based on adding a second regularization term in the objective function of a Fuzzy C-Regression Model (FCRM) clustering algorithm in order to take into account noisy data. In addition, a new error measure is used in the objective function of the FCRM algorithm, replacing the one used in this type of algorithm. Then, particle swarm optimization is employed to finally tune parameters of the obtained fuzzy model. The orthogonal least squares method is used to identify the unknown parameters of the local linear model. Finally, validation results of two examples are given to demonstrate the effectiveness and practicality of the proposed algorithm

Sliding Mode Observers Based-Simultaneous Actuator and Sensor Faults Estimation for Linear Parameter Varying Systems

This paper proposes a scheme to estimate actuator and sensor faults simultaneously for a class of linear parameter varying system expressed in polytopic structure where its parameters evolve in the hypercube domain. Transformed coordinate system design is adopted to decouple faults in actuators and sensors during the course of the system’s operation coincidentally, and then two polytopic subsystems are constructed. The first subsystem includes the effect of actuator faults but is free from sensor faults and the second one is affected only by sensor faults. The main contribution is to conceive two polytopic sliding mode observers in order to estimate the system states and actuator and sensor faults at the same time. Meanwhile, in linear matrix inequality optimization formalism, sufficient conditions are derived with H∞ performances to guarantee the stability of estimation error and to minimize the effect of disturbances. Therefore, all parameters of observers can be designed by solving these conditions. Finally, simulation results are given to illustrate the effectiveness of the proposed simultaneous actuator and sensor faults estimation

An H∞ sliding mode observer for Takagi–Sugeno nonlinear systems with simultaneous actuator and sensor faults An

This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two discontinuous terms to solve the problem of simultaneous faults. Sufficient stability conditions in terms linear matrix inequalities are achieved to guarantee the stability of the state estimation error. The observer gains are obtained by solving a convex multiobjective optimization problem. Simulation examples are given to illustrate the performance of the proposed observe